I suppose it depends if "their" implies possession or ownership. It would be correct to say they possess this data. It's dicier to say they own it, much like I "possess" the apartment I rent but I do not "own" it.

Regardless, digital file possession and ownership doesn't map cleanly to our language. I technically don't own any Kindle books I buy, I can't share them, yet I clearly have access to an ebook. So I both do and don't currently possess said book.